Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q1 up through 2018 Q1. The test period is a forecast for 2018 Q2 and includes comparison to the observed median rent estimates for data collected in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-07-03




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 307.9453 208.7554 202.8790 193.5590 193.5437
Training 324.2904 145.9141 145.9562 147.2612 146.1490



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 252.8729 149.3779 148.4784 141.5393 141.4224
Training 261.4572 100.9766 100.6866 102.2923 101.5392



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -230.4437 -872.8758 -871.7695 -874.5404 -875.875



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -230.0655 -845.3891 -844.3364 -847.8235 -848.7253

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.4504 6.3451 82.3883 94.3203 107.3392 94.1694
Precision for idtract 30.7244 4.2509 23.1165 30.4724 39.8230 30.0119
Precision for idqtr 3704.6708 3774.0461 555.1018 2589.2781 13619.6753 1361.1160
Rho for idqtr 0.2605 0.3581 -0.4721 0.2856 0.8484 0.3946
Precision for idqtr1 14301.7423 17584.8007 273.1949 8209.2304 61744.3916 355.9311



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 93.8917 6.3341 81.9496 93.7160 106.8857 93.4176
Precision for idtract (iid component) 89.1249 21.3833 54.4113 86.6700 138.0413 81.9914
Precision for idtract (spatial component) 90.8711 29.0415 47.2708 86.4316 159.9897 78.2506
Precision for idqtr 3858.3700 4054.8429 567.3181 2653.8280 14469.1195 1381.3683
Rho for idqtr 0.2769 0.3551 -0.4614 0.3071 0.8507 0.4351
Precision for idqtr1 13449.1294 16720.0692 259.8289 7675.2631 58131.8642 347.1966



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.3039 6.3950 82.2170 94.1394 107.3907 93.8810
Precision for idtract (iid component) 89.5254 21.5279 54.3630 87.1316 138.6381 82.5833
Precision for idtract (spatial component) 90.7663 29.0703 47.2895 86.2365 159.9716 77.9197
Precision for idqtr 3917.9019 4058.4687 587.4699 2714.5332 14559.7794 1426.2925
Rho for idqtr 0.2629 0.3568 -0.4686 0.2885 0.8479 0.3987
Precision for idqtr1 13538.0758 16841.2369 244.2094 7676.4899 58469.1492 303.0846
Precision for idtractqtr 19038.0980 18495.7186 1371.6082 13630.8124 67834.5139 3784.7111

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)